Patriarch Raphael had served for nearly 10 years as archbishop of Kirkuk.
The Catholic charity Aid to the Church in Need welcomed the appointment, as its director of Middle East Projects, Father Andrzej Halemba, called him the "right man for the job."
He said: "Louis Sako is a messenger of peace and dialogue. He is most definitely a man of courage. Problems only seem to make him work harder."
Father Halemba added: "Christians are continuing to leave the country. There must be some personality who can give them back their hope.
"Louis Sako is the right man for the job."
Staff of the charity recalled how as a young priest, Father Sako took his petition to teach Christianity in his parish all the way to President Saddam Hussein who met him to discuss the matter.
John Pontifex, ACN UK Head of Press and Information, who has known the new patriarch for nearly 10 years, meeting him in Kirkuk, Rome and the UK, said: "Archbishop Sako is a man who encompasses so many different qualities – on the one hand rigorous scholarship and on the other abiding pastoral concern.
"He is passionate in his defense of the truth and the needs of the people – these are the hallmarks of this man who is always so humble.
"But above all, the new patriarch is a man of faith, who is committed to the way of the Lord. For these reasons, his election will I am sure give the people great hope."
Christians in Iraq are less than 300,000, down from below 800,000 a decade ago and 1.4 million at the last census in 1987.
Reports released last year showed that since 2003 more than 70 churches in Iraq have been attacked, most of them bombed – 44 in Baghdad and 19 in the northern city of Mosul.
In interviews given since his election, Patriarch Raphael I has pledged to work for unity – not just within the Chaldean Church but also with Orthodox communities.
Stressing the Chaldean Church’s many difficulties in times of huge upheaval and oppression, he told AsiaNews: "Together with the bishops of the Chaldean Church, we shall work for unity and renewal."
Patriarch Raphael I Sako replaces Patriarch Cardinal Emmanuel III Delly, 85, who resigned for reasons of age.